Divisibility Rules for 2, 3, 4, 5, 6, 8, 9 and 10

Start with the final digit

An integer is divisible by 2 when its final decimal digit is even. It is divisible by 5 when the final digit is 0 or 5, and by 10 when the final digit is 0. For 234, the last digit 4 confirms divisibility by 2 but rules out 5 and 10.

For divisibility by 4, inspect the last two digits. For divisibility by 8, inspect the last three. Thus 1236 is divisible by 4 because 36 is, but 1236 is not divisible by 8 because 236 leaves remainder 4.

Use the digit sum for 3 and 9

The digits of 234 add to 9. Because 9 is divisible by both 3 and 9, so is 234: 234 ÷ 3 = 78 and 234 ÷ 9 = 26. The digits of 235 add to 10, so 235 is divisible by neither 3 nor 9.

To test 6, combine the tests for 2 and 3. Two hundred thirty-four is even and divisible by 3, so it is divisible by 6. Being divisible by only one of those two factors is not enough.

Do not extend a rule beyond its scope

A digit sum does not generally test divisibility by 7. Similarly, the last two digits are enough for 4 but not for every divisor. When no suitable rule is at hand, ordinary division with remainder is reliable.

Every number page provides quotients and remainders for divisors 2 through 12. A zero remainder confirms exact divisibility; a nonzero remainder tells you how far the nearest lower multiple falls short.

Check the mathematical definitions

For fractions, percentages and worked arithmetic, see OpenStax Prealgebra. For number definitions, see OpenStax on prime and composite numbers and Wolfram MathWorld on digital roots. Worked examples on this page are calculated for this guide.